Why should we rather work with volume time?

Many articles that I came across use volume time $$v$$ in their computations since the market activity level varies substantially throughout the day (intraday volume and volatility patterns), which is the cumulative volume function defined by $$v=0$$ at the open and $$v=1$$ at the close.

Could anyone explain the purpose of introducing such a variable? What's the problem with a varying volume profile?

Thanks